Adaptive Wavelet Rendering

Transcription

1 Adaptive Wavelet Rendering Author: Ryan Overbeck Craig Donner Ravi Ramamoorthi Presenter: Guillaume de Choulot 1

2 The Problem (combined effects) 2 Pixel Area Camera Aperture Area Light Pixel = 6D

3 General combinations of effects Antialiasing Depth of field Antialiasing Depth of field Motion Blur Antialiasing Depth of field Area Lighting Antialiasing Depth of field Envir. Lighting Antialiasing Depth of field Area Lighting 1 Bounce GI 4D 5D 6D 6D 8D 3

4 Monte Carlo Problem (1/1) Noisy for low sample counts (smooth regions) 32 Samples Per Pixel 4

5 Monte Carlo Problem (2/2) Requires hundreds to thousands of samples 512 Samples Per Pixel 5

6 Our Solution (important sampling) Adaptive Wavelet Rendering 32 Samples Per Pixel (average) 6

7 Features of Adaptive Wavelet Rendering Low Sample Counts Converges from smooth 7

8 Features of Adaptive Wavelet Rendering Low Sample Counts Converges from smooth Near Reference: 32 samples per pixel 8 Average of 32 Samples Per Pixel

9 Features of Adaptive Wavelet Rendering Low Sample Counts Converges from smooth Near Reference: 32 samples per pixel Smooth Preview Quality: 8 samples per pixel 9 Average of 8 Samples Per Pixel

10 Features of Adaptive Wavelet Rendering Low Sample Counts Efficient Less samples gives Faster render times 10

11 Features of Adaptive Wavelet Rendering Low Sample Counts Efficient Less samples gives Faster render times 11 Monte Carlo (512 spp) >6 Hours > 6 Hours Monte Carlo 512 Samples Per Pixel

12 Features of Adaptive Wavelet Rendering Low Sample Counts Efficient Less samples gives Faster render times 12 Monte Carlo (512 spp) Our Method (32 spp) >6 Hours 34 minutes 34 Minutes Adaptive Wavelet Rendering 32 Samples Per Pixel (average)

13 Features of Adaptive Wavelet Rendering Low Sample Counts Efficient General Insensitive to problem dimensionality General combinations of effects 13 Pixel Area 32 Samples per pixel (average) 15 minutes Camera Aperture Area Light 8D Hemisphere

14 14

15 15 The Insight (Important sampling)

16 Variance is often local Variance High Low 16

17 Send more samples to high variance Sample Count High Our method 32 Samples Per Pixel (average) Low 17

18 Two forms of variance Smooth Variance Edges 18

19 Variance from image space: edges High Variance Low 19

20 Focused samples to image edges Final Result High Samples Low 20

21 Variance from other dims: smooth Difficult for Monte Carlo High Variance Low 21

22 22 Smooth is easier in multi-scale

23 Smooth is easier for wavelets wavelet synthesis calculate pixel 23

24 Coarse Sampling of Smooth Regions Final Result High Samples Low 24

25 Algorithm Outline Start: 4 Samples per Pixel Adaptive Sampling Reconstruction 25

26 Related Work 26 Adaptive sampling Bolin & Meyer 1998, Whitted 1980, Mitchell 1987, Veach and Guibas 1997, Walter et al (Multidim Lightcuts) Multi-scale Keller 2001 (Hierarchical MC), Heinrich and Sindambiwe 1999, Guo 1998, Bala et al. 2003, Walter et al (Lightcuts), Perona and Malik 1990 Wavelet sampling and reconstruction Our method works well for both edges and smooth regions

27 27 Background: Wavelets

28 Wavelets made of 2 functions Scale Wavelet Low Pass (smooth) Band Pass (edges) 28

29 Wavelet Hierarchy (1D) Scale Wavelet Low Pass (smooth) Band Pass (edges) 29

30 Wavelet Hierarchy (1D) Scale Wavelet k = 3 k = 2 k = 1

31 1D Tensor Product 2D Basis k = 3 scale scale = scale-scale scale wavelet = scale-wavelet wavelet scale = wavelet-scale wavelet wavelet = wavelet-wavelet

32 Wavelet used k = 4 JPEG 2000 compression 32

33 Wavelets Basis (& DWT) Wavelets (Multi-scale basis) VS Pixel Basis Multi scale: coefficient/wavelet expressed in different scale Discret Wavelet Transform (DWT): 1) Pixels Wavelets coefficient (Analysis) 2) Wavelets Pixels (Synthesis) 33

34 Wavelet Hierarchy k=5 =4 k=3 k=2 k=1 scale-scale scale-wavelet wavelet-scale wavelet-wavelet Smooth regions Edges 34

35 III) Algorithm Outline 0) Start: 4 Samples per Pixel (skipped) 1) Adaptive Sampling 2) Reconstruction 35

36 1) Adaptive Sampling Insert all scale coefficients into a priority queue While more samples: Send samples to highest priority coefficient Update priority queue The problem: How to compute priority for each scale coefficient? 36

37 37 scale-scale

38 38 scale-scale

39 Wavelet synthesis is smoothing scale-scale 39

40 Coarse scale captures smoothness Smooth Region scale-scale 40

41 Edges are in the fine scale Smooth Region Edges Smoothed out scale-scale 41

42 Adaptive Sampling Goals: In smooth regions, more samples to coarse coefficients Near edges, more samples to fine coefficients Solution: Compute priority based on variance and smoothness 42

43 Start with Scale Coefficients Variance Scale Variance low high 43

44 Smooth variance grows fine to coarse Scale Variance Smooth Region Higher low high 44

45 Edge variance stays the same Scale Variance Edge Region Same low high 45

46 Squared wavelet magnitudes Scale Variance (Wavelet Magnitude) 2 low high 46

47 Edge wavelets grow fine to coarse Scale Variance (Wavelet Magnitude) 2 Edge Region Higher (ok) low high 47

48 Smooth wavelets stay the same Scale Variance (Wavelet Magnitude) 2 Smooth Region Same (problem) low high 48

49 Priority equals the difference Scale Variance (Wavelet Magnitude) 2 Priority - = low high 49

50 Edges: Higher priority at fine scales Scale Variance (Wavelet Magnitude) 2 Priority Edge Region - = Higher low high 50

51 Smooth: Higher priority at coarse scales Scale Variance (Wavelet Magnitude) 2 Priority Smooth Region - = Higher low high 51

52 After adaptive sampling Smooth Region in Coarse Scale Accurate 52

53 After adaptive sampling Smooth Region in Coarse Scale Accurate Edges in Fine Scale 53 Accurate

54 After adaptive sampling Smooth Region in Coarse Scale Smooth Region in Fine Scale Accurate Noisy Edges in Fine Scale 54 Accurate

55 Reconstruction: smooth away fine scale noise Smooth Region in Coarse Scale Smooth Region in Fine Scale Accurate Noisy Edges in Fine Scale 55 Accurate

56 Wavelets capture edges scale-scale scale-wavelet wavelet-scale wavelet-wavelet Edges 56

57 Wavelets capture edges and Noise scale-scale scale-wavelet wavelet-scale wavelet-wavelet Edges and Noise 57

58 Algorithm Outline 0) Start: 4 Samples per Pixel 1) Adaptive Sampling -> 2) Reconstruction 58

59 Wavelet Reconstruction Remove noise by suppressing wavelet magnitudes How? Choose smoothest image which fits samples 59

60 Monte Carlo: statistics High +Standard Deviation (estimate of Error) Mean -Standard Deviation Low 60

61 Monte Carlo: statistics High +Standard Deviation Valid Range Mean Monte Carlo Estimate -Standard Deviation Low 61

62 For pixel: High +Standard Deviation Pixel Mean -Standard Deviation Luminance Low 62

63 For pixel: luminance High +Standard Deviation Pixel Mean -Standard Deviation Luminance Low 63

64 For pixel: luminance High +Standard Deviation Pixel Mean -Standard Deviation Brightness Low 64

65 For wavelet: High +Standard Deviation Wavelet Coefficient Mean -Standard Deviation Low 65

66 For wavelet: Smoothness High +Standard Deviation Wavelet Coefficient Mean -Standard Deviation Smoothness Low 66

67 Take the smoothest value High +Standard Deviation Wavelet Coefficient Mean Our Estimate -Standard Deviation Smoothness Low 67

68 68 Reconstruction computation?!

69 69 After Sampling

70 70 After Reconstruction

71 71 Results (1/2)

72 72 Results (2/2)

73 Limitations (1/3) Wavelet artifacts when not enough samples Ringing around edges Ringing Our Method Noise samples per pixel (avg.) Monte Carlo

74 Limitations (2/3) Wavelet artifacts when not enough samples Ringing around edges Overly smoothing Too Smooth Our Method Noise samples per pixel (avg.) Monte Carlo

75 Limitations (3/3) Wavelet artifacts when not enough samples Ringing around edges Overly smoothing Potential solutions Variance reduction (path splitting, QMC, etc.) Reduce smoothing during reconstruction Use depth and normals to improve statistics Use more samples 75

76 Conclusion/Summary Sample and reconstruct in wavelet basis Features Low Sample Counts Efficient General Best for smooth image features 76